Question

Assume that CAPM is a good representation of the risk-return relationship. You are holding a portfolio of stocks. The portfolio’s standard deviation is 40% and its correlation with "M" is 0.8. The risk free rate is 2.5%, the expected market return is 12%, and the standard deviation of the market return is 17.6%.

1. What is the expected return on your portfolio?
2. Is this portfolio efficient? How can you tell?
3. If this portfolio is not efficient, how much risk reduction could you achieve, at no sacrifice in expected return, by making your portfolio an efficient one?
4. Now suppose that you are comfortable with the overall risk of your current portfolio, but want to improve your return by making your portfolio efficient. What would be the return on the efficient portfolio with the same overall risk as your current portfolio?

Answer 1

I have answered the question below

Please up vote for the same and thanks!!!

Do reach out in the comments for any queries

Answer:

1.

Beta formula is given by correlation * std dev of the portfolio/ std dev of the market
Beta=0.8*40%/17.6%=1.818

According to CAPM => re = rf + beta(rm - rf)

Expected returns=2.5%+1.818181818*(12%-2.5%)=19.77273%

2.
This is not an efficient portfolio market offers higher return at same risk i.e, market has higher Sharpe ratio

3.
Let w be the weight in market and 1-w be the weight in risk free rate
w*12%+(1-w)*2.5%=19.77273%
=>w=(19.77273%-2.5%)/(12%-2.5%)
=>w=1.818182105

Standard deviation=1.818182105*17.6%=32.00%

Risk reduction=40%-32%=8%

4.

=40%/17.6%*12%+(1-40%/17.6%)*2.5%
=24.09091%